RL time constant

An inductor resists sudden changes in current the way a heavy flywheel resists sudden changes in speed — so when you switch a resistor-and-inductor circuit on or off, the current ramps up or coasts down exponentially rather than snapping instantly. The time constant for this is τ = L/R, and it sets how stubbornly the current clings to its old value.

After one time constant the current has reached about 63% of its final value (or decayed to 37% when switching off), and after roughly 5τ it has essentially settled. Note the inverted form compared with RC: here a bigger resistance makes the transient faster, because more resistance means the inductor's stored energy bleeds away sooner. This is why switching an inductive load (a relay coil, a motor) produces a dangerous voltage spike — the current can't stop instantly, so the inductor flings its energy into whatever path remains, which is why we add flyback diodes.